Abstract

Two parallel tune measurement systems are installed at GSI SIS-18 based on diﬀerent principles. The ﬁrst is called the Tune, Orbit and POSition measurement system TOPOS. Its working principle involves direct digitization of BPM signals at 125 MSa/s, which is used for online bunch-by-bunch position calculation in FPGAs. In the course of this work, position calculation algorithms were developed and studied for real time implementation in the TOPOS FPGAs. The regression ﬁt algorithm is found to be more eﬃcient and robust in comparison to previously used weighted mean algorithm with the baseline restoration procedure. The second system is the Baseband Tune measurement system referred to as BBQ system. The operational principle of this system was conceived at the CERN Beam Instrumentation group and is based on direct diode detection. In the framework of this work, this system was optimized and brought into operation at GSI SIS-18. Front-end data from both systems are used to calculate the tune spectrum every 250−5000 beam revolutions or turns within SIS-18 based on the resolution requirement and the mode of operation. Advanced non-parametric spectrum estimation method like amplitude Capon estimator is compared to the conventional DFT based methods in terms of resolving power and computational requirements for the calculated spectrum. Further the TOPOS and BBQ systems are compared and characterized in terms of sensitivity, reliability and operational usage. The results from both systems are found to be consistent with each other and have their favoured regimes of operation. The eﬀects on tune spectra obtained from both systems were studied with diﬀerent types of excitations with excitation power levels up to 6 mW/Hz. These systems in association with other beam diagnostic devices at SIS-18 were used to conduct extensive experiments to understand the eﬀect of high intensity beams on the tune spectrum. These careful measurements recorded all the relevant beam parameters,thus leaving out no “free parameters”. Several important results were established in course of these experiments. Coherent tune shifts in dependence of intensity gave direct measurements of transverse machine impedances. The high resolution tune spectrum allowed identiﬁcation of higher order head-tail modes. The relative spectral positions of these head-tail modes when compared with the analytical theory based on the “square well airbag model” gave a direct measurement of the incoherent tune spread in bunched beams. The measurements agreed well with the perturbative treatment applied in the theory only for space charge parameter in the range qsc < 4 after which signiﬁcant deviations from the theoretical predictions occur. These deviations were understood by using self-consistent simulations and are attributed to the unaccounted role of the pipe impedances in Landau damping of head-tail modes. A novel chromaticity measurement method is demonstrated using temporal separation of each head-tail mode using chirp excitation. Other applications of the parallel tune measurement systems such as linear betatron coupling measurements or tune measurements during acceleration ramps are demonstrated. This work forms a basis for understanding beam dynamics at GSI SIS-18 for high beam currents.

Two parallel tune measurement systems are installed at GSI SIS-18 based on diﬀerent principles. The ﬁrst is called the Tune, Orbit and POSition measurement system TOPOS. Its working principle involves direct digitization of BPM signals at 125 MSa/s, which is used for online bunch-by-bunch position calculation in FPGAs. In the course of this work, position calculation algorithms were developed and studied for real time implementation in the TOPOS FPGAs. The regression ﬁt algorithm is found to be more eﬃcient and robust in comparison to previously used weighted mean algorithm with the baseline restoration procedure. The second system is the Baseband Tune measurement system referred to as BBQ system. The operational principle of this system was conceived at the CERN Beam Instrumentation group and is based on direct diode detection. In the framework of this work, this system was optimized and brought into operation at GSI SIS-18. Front-end data from both systems are used to calculate the tune spectrum every 250−5000 beam revolutions or turns within SIS-18 based on the resolution requirement and the mode of operation. Advanced non-parametric spectrum estimation method like amplitude Capon estimator is compared to the conventional DFT based methods in terms of resolving power and computational requirements for the calculated spectrum. Further the TOPOS and BBQ systems are compared and characterized in terms of sensitivity, reliability and operational usage. The results from both systems are found to be consistent with each other and have their favoured regimes of operation. The eﬀects on tune spectra obtained from both systems were studied with diﬀerent types of excitations with excitation power levels up to 6 mW/Hz. These systems in association with other beam diagnostic devices at SIS-18 were used to conduct extensive experiments to understand the eﬀect of high intensity beams on the tune spectrum. These careful measurements recorded all the relevant beam parameters,thus leaving out no “free parameters”. Several important results were established in course of these experiments. Coherent tune shifts in dependence of intensity gave direct measurements of transverse machine impedances. The high resolution tune spectrum allowed identiﬁcation of higher order head-tail modes. The relative spectral positions of these head-tail modes when compared with the analytical theory based on the “square well airbag model” gave a direct measurement of the incoherent tune spread in bunched beams. The measurements agreed well with the perturbative treatment applied in the theory only for space charge parameter in the range qsc < 4 after which signiﬁcant deviations from the theoretical predictions occur. These deviations were understood by using self-consistent simulations and are attributed to the unaccounted role of the pipe impedances in Landau damping of head-tail modes. A novel chromaticity measurement method is demonstrated using temporal separation of each head-tail mode using chirp excitation. Other applications of the parallel tune measurement systems such as linear betatron coupling measurements or tune measurements during acceleration ramps are demonstrated. This work forms a basis for understanding beam dynamics at GSI SIS-18 for high beam currents.